Concept Architecture
Concept
Theoretically, Immortal Time is a period of follow-up during which the outcome of interest cannot occur by design or by definition of the study. The concept arises in observational epidemiology and survival analysis and is closely associated with time-dependent exposure assessment. Immortal time exists because participants must survive or remain event-free throughout this interval in order to be classified into a particular exposure group. Failure to account for immortal time introduces immortal time bias, leading to systematically biased estimates of treatment effectiveness.
Mathematically, Immortal Time is represented as a time interval during which an individual's exposure status is not yet established, and during which the event cannot contribute to the exposed risk set. Correct statistical representation requires exposure status to be modelled as a time-dependent covariate so that individuals contribute person-time to the appropriate risk set before and after exposure. Standard Cox proportional hazards models incorporating time-dependent covariates provide unbiased estimation of treatment effects under this framework.
In practice, Immortal Time most commonly occurs in observational studies evaluating medications, procedures or healthcare interventions where treatment initiation occurs after cohort entry. Participants contribute unexposed person-time until treatment begins and exposed person-time thereafter. Appropriate handling requires time-dependent survival models or equivalent analytical methods. Correct treatment of immortal time is essential in comparative effectiveness research and health economic evaluations that use observational evidence to estimate long-term treatment effects.
Purpose
Used to identify periods of guaranteed event-free follow-up and ensure that survival analyses correctly allocate person-time, thereby preventing immortal time bias and producing valid estimates of treatment effectiveness.
Mathematical Formulae
Primary Formula
Time-dependent Cox proportional hazards model:
h(t�X(t)) = h?(t) ? exp(?X(t))
where:
- h(t�X(t)) = hazard at time t
- h?(t) = baseline hazard
- X(t) = time-dependent exposure status
- ? = treatment effect
Supporting Formulae
Person-time:
PT = ? t?
Hazard Ratio:
HR = exp(??)
Time-dependent exposure indicator:
X(t) = {0, t < T?
1, t � T?}
where T? is the treatment initiation time.
Related Mathematical Methods
- Time-Dependent Cox Regression
- Survival Analysis
- Time-Varying Covariates
- Left Truncation
- Risk Set Construction
- Hazard Ratio Estimation
- Counting Process Models
Example
A retrospective cohort study evaluates the effect of a biologic therapy on mortality. Patients enter the cohort at diagnosis, but treatment is initiated an average of six months later. A patient who dies before receiving treatment cannot be classified as treated. Therefore, the first six months constitute immortal time for treated patients. The analysis models treatment as a time-dependent covariate so that follow-up before treatment contributes to the untreated group and follow-up after treatment contributes to the treated group, avoiding immortal time bias.
Excel Implementation
| Function | Example Formula | Health Economics Application |
|---|---|---|
| IF | =IF(FollowUpTime>=TreatmentStart,1,0) | Create a time-dependent exposure indicator. |
| MAX | =MAX(0,FollowUpTime-TreatmentStart) | Calculate exposed person-time. |
| MIN | =MIN(FollowUpTime,TreatmentStart) | Calculate unexposed person-time before treatment. |
| SUM | =SUM(PersonTimeRange) | Calculate total person-time. |
| COUNTIFS | =COUNTIFS(Status,1,Exposure,1) | Count events occurring during exposed follow-up. |
VBA (Optional)
VBA can automate splitting follow-up into exposed and unexposed person-time and generate datasets suitable for time-dependent survival analyses.
Sources
- Suissa S. Immortal Time Bias in Observational Studies of Drug Effects. Pharmacoepidemiology and Drug Safety.
- Hern�n MA, Robins JM. Causal Inference: What If.
- Rothman KJ, Greenland S, Lash TL. Modern Epidemiology.
- Therneau TM, Grambsch PM. Modeling Survival Data: Extending the Cox Model.
- NICE. Health Technology Evaluation Manual.
- Briggs A, Claxton K, Sculpher M. Decision Modelling for Health Economic Evaluation.
Related Concepts (2)
Library
Publications
1
Good Practices for Real-World Data Studies of Treatment and/or Comparative Effectiveness: Recommendations from the Joint ISPOR-ISPE Special Task Force on Real-World Evidence in Health Care Decision Making — Berger, Sox, Willke, Brixner, Eichler, Goettsch, Madigan, Makady, Schneeweiss, Tarricone, Wang, Watkins & Mullins, Vol. 20, No. 8 ed., 2017 (Value in Health)
The joint ISPOR-ISPE recommendations on good procedural practice for real-world data studies (observational studies and registries) used to inform healthcare decisions — study registration, replicability and stakeholder involvement — the reference for RWE credibility in HTA.
Journal ArticleView source →
Frequently Asked Questions (6)
What is immortal time?
A period of follow-up during which, due to how exposure groups were defined, a participant could not possibly have experienced the outcome.
Source: Suissa 2008
Why is the period called immortal time?
The period is called immortal because, by the way the study is set up, a participant simply could not have had the outcome during it and had to survive event-free through it to be classified as they were. For instance, if patients count as treated only once they fill a prescription, the time before filling it is one they were guaranteed to survive to reach that point. No event could occur in that window by definition, hence immortal. It is a stretch of guaranteed survival built in by classification. Suissa (2008) describes this.
Source: Suissa 2008
How does immortal time arise?
Immortal time arises when group membership depends on an event that occurs after follow-up begins, such as receiving a treatment, so that participants classified as treated must have survived event-free until that event. The span between the start of follow-up and the defining event is immortal, since the outcome could not have occurred during it without preventing the classification. This period, guaranteed to be event-free by the way the groups are defined, is the immortal time, and mishandling it in the analysis leads to bias.
Source: Suissa 2008
Why does immortal time cause bias?
Immortal time causes bias when the guaranteed event-free period is misattributed, for example counted as exposed follow-up for the treated group, because it lowers the apparent event rate in that group by adding time during which the outcome could not occur. This makes the treatment appear protective when the difference is an artefact of the classification and time handling, not a real effect. Because the bias is systematic and can be substantial, immortal time bias can seriously distort estimates of treatment effect in observational studies unless the time is classified correctly.
Source: Rothman, Greenland & Lash 2008
How is immortal time bias avoided?
Immortal time bias is avoided by classifying person-time correctly according to when exposure actually begins, using time-varying exposure definitions so that follow-up before the defining event is not counted as exposed, and by using analytic approaches, such as landmark analysis or time-dependent models, that handle the timing appropriately. Aligning the start of follow-up with exposure status and not attributing the immortal, pre-exposure time to the exposed group removes the bias. So careful, correct handling of time-related exposure definitions is the way to prevent immortal time bias.
Source: Suissa 2008
Where does immortal time commonly occur?
Immortal time commonly occurs in observational pharmacoepidemiological and cohort studies where exposure groups are defined by an event happening after follow-up starts, such as filling a prescription, undergoing a procedure, or responding to treatment, which requires the participant to survive event-free to that point. Studies comparing treated with untreated patients, or responders with non-responders, are especially prone. Any design in which group membership depends on surviving long enough to meet a time-dependent criterion can generate immortal time, so recognising these situations is important for avoiding immortal time bias.
Source: Suissa 2008
Trust Record
Verified by Dr Darrin Baines
British health economist
Professional identity: darrinbaines.org
Verification date: 14 Nov 2025
Content version: 1.0.0
Canonical Identity
- Persistent URI
- https://healtheconomics.wiki/concept/immortal-time
- Term code
- HE-ES-CTM-040
Stable URI · Machine-readable · Resolvable · CC BY 4.0